How to get dirtiness on a simple texture?
I would recommend establishing a paint set up in Blender first on the model by painting details on the model in the 3d view using Texture Paint mode, and then take the saved image textures into Photoshop to further build on the initial block out. Here in the picture I have used a cloud texture on a texture paint brush set to multiply and Rake and Random for the stroke, and painted grunge burns on the areas where I cloned the image texture into my basic canvas texture.

One thing to note is that you can use Photoshop to paint in 3d view, so you might just try importing your model as .obj with your basic material and texture and then adding a layer in photoshop, doing your detail work there.